At some time when you want chat with any g talk user urgently and g talk user is showing offline in google talk status doesn't mean that your friend is really offline.

Ya its fact Google talk user might be in invisible mode in g talk, so displaying the offline icon Google talk. At G talk tips but know now How I can detect invisible g talk user status (original status) .
Follow these step

Set the chat as off the record with target user how? ok Click on left corner of g talk messanger , Down arrow and select Go Off the record

you will see this message "You are now off the record (from now on, chats with ( gtalk user name ) will not be saved in ( gtalk user name ) 's Gmail account or yours) and ther are two option Learn more Cancel "

Note : This should be done when other gtalk user is online.

Now try sending chat to g talk user when he is invisible or offline.

In return if you see message in red color "“ did not receive your chat”. that meansyour gtalk friend is really offline in Gtalk. But if you have not receive error message from g talk it means other side is invisible g talk user .

But always keep in mind that when a chat is set off the record, it will no longer get stored in your Gmail account. If g talk user is offline, your chat message will go to inbox as a mail. But when set chat off the record g talk can’t be delivered to inbox as mail